The Optimal Martingale Transport Problem With Additional Information about Variance of the Returns

We investigate the optimal transport problem with martingale constraints and its application to model-independent price bounds for financial derivatives. The novelty of this paper is the additional consideration of information... [ view full abstract ]

We investigate the optimal transport problem with martingale constraints and its application to model-independent price bounds for financial derivatives. The novelty of this paper is the additional consideration of information about the variance of the returns of an underlying discrete-time stochastic process. This additional information is well motivated by observations of prices on financial markets. Our theoretical results comprise a dual version of the modified problem. Our empirical results indicate that tighter price bounds for exotic options can be obtained. In this respect, our results also have important implications for the practical applicability and relevance of model-independent price bounds.